Abstract:Biological Networks have received much attention in recent years, but statistical tools for network analysis are still in their infancy. In this paper we focus on Protein Interaction Networks (PINs) that typically comprise thousands of proteins and interactions. PINs are the result of long evolutionary histories. Here we adopt simple mathematical models that capture essentials of protein evolution and develop statistical methods to estimate evolutionary PIN parameters. Our initial approach is based on a recursion for the likelihood, but it becomes computationally intractable for reasonably sized networks. Our second approach is based on summary statistics and likelihood-free inference. We discuss problems with selection of summaries, convergence, and credibility and apply the methods on Helicobacter pylori and Plasmodium falciparum data.